Symmetrised M-estimators of multivariate scatter. (English) Zbl 1122.62048

Summary: We introduce a family of symmetrised M-estimators of multivariate scatter. These are defined to be M-estimators only computed on pairwise differences of the observed multivariate data. The symmetrised Huber’s M-estimator and L. Dümbgen’s [Ann. Inst. Stat. Math. 50, No. 3, 471–491 (1998; Zbl 0912.62061)] estimator serve as our examples. The influence functions of the symmetrised M-functionals are derived and the limiting distributions of the estimators are discussed in the multivariate elliptical case to consider the robustness and efficiency properties of estimators. The symmetrised M-estimators have the important independence property; they can therefore be used to find the independent components in the independent components analysis (ICA).


62H12 Estimation in multivariate analysis
62G35 Nonparametric robustness
62E20 Asymptotic distribution theory in statistics
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference


Zbl 0912.62061


Full Text: DOI


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